Jammu and Kashmir Board Solutions for Chapter: Mensuration, Exercise 19: Miscellaneous Exercise

The volume of a cube in ${\mathrm{cm}}^3$ is equal to curved surface area of a cube in ${\mathrm{cm}}^2$, then what is the side of the cube.

The surface area of a cube is $24 {\mathrm{cm}}^2$. Two same cubes were joined end to end to form a cuboid. Find the surface area of the cuboid formed.

The volume of a cuboid is $27 {\mathrm{cm}}^3$. Find its surface area.

How many minimum numbers of wooden cuboids of size $2 \mathrm{cm}\times 3 \mathrm{cm} \times 4 \mathrm{cm}$ can make a smallest cube? Cutting is allowed. Also find the surface area and volume of cube formed.

Find the area of trapezium $BORD$; $BO\parallel DR$ in which $BO=11 \mathrm{cm}, BD=6 \mathrm{cm}, DR=5 \mathrm{cm}$ and $RO=5 \mathrm{cm}$. (correct up to two decimal places)

A liquid in a cuboid of size $11 \mathrm{cm}\times 9 \mathrm{cm}\times 4 \mathrm{cm}$ had to be poured into small cylindrical bottles of diameter $4 \mathrm{cm}$ and height $3.5 \mathrm{cm}$. How many such bottles are required to empty the cuboid? (Take $\pi =\frac{22}{7}$)

A brimful of water cylinder whose radius is $7 \mathrm{cm}$ and height $6 \mathrm{cm}$. An iron cuboid of size $3 \mathrm{cm}\times 4 \mathrm{cm}\times 5 \mathrm{cm}$ is slowly put into it. How much water will drop out? How much water remained in the cylinder?

The radius of a cylinder is doubled and the height is halved. Find the ratio of curved surface areas and volumes of the original cylinder to that of a new cylinder formed?